diff --git a/Triangulation/doc/Triangulation/CGAL/Delaunay_triangulation.h b/Triangulation/doc/Triangulation/CGAL/Delaunay_triangulation.h
index 322cfb51756..e5f08dd1d5e 100644
--- a/Triangulation/doc/Triangulation/CGAL/Delaunay_triangulation.h
+++ b/Triangulation/doc/Triangulation/CGAL/Delaunay_triangulation.h
@@ -125,8 +125,8 @@ value of `lt`:
 <DT><B>`OUTSIDE_AFFINE_HULL`</B><DD> Point
 `p` is inserted so as to increase the current dimension of the Delaunay
 triangulation.
-<DT><B>`ON_VERTEX`</B><DD> The position of the vertex `v` described by `f`
-is set to `p`. `v` is returned. <DT><B>Anything else</B><DD> The point `p`
+<DT><B>`ON_VERTEX`</B><DD> The triangulation remains unchanged.
+<DT><B>Anything else</B><DD> The point `p`
 is inserted. the full cell `c` <I>is assumed</I> to be in conflict
 with `p`.
 </DL>
diff --git a/Triangulation/doc/Triangulation/CGAL/Triangulation.h b/Triangulation/doc/Triangulation/CGAL/Triangulation.h
index 1d7b0e1a65d..32188c44323 100644
--- a/Triangulation/doc/Triangulation/CGAL/Triangulation.h
+++ b/Triangulation/doc/Triangulation/CGAL/Triangulation.h
@@ -556,8 +556,7 @@ Inserts point `p` into the triangulation and returns a handle to the
 `Vertex` at that position. The action taken depends on the value of
 `loc_type`:
 
-<DL> <DT><B>`ON_VERTEX`</B><DD> The point of the
-p`Vertex` described by `f` is set to `p`.
+<DL> <DT><B>`ON_VERTEX`</B><DD> The triangulation remains unchanged.
 <DT><B>`IN_FACE`</B><DD> The point `p` is inserted in the `Face f`.
 <DT><B>`IN_FACET`</B><DD> The point `p` is inserted in the `Facet ft`.
 <DT><B>Anything else</B><DD> The point `p` is inserted in the triangulation according to the value